Question

The difference between compound interest and

simple interest on the sum of ` 7500 for 2 years

at the same rate of interest is ` 108. The rate of

interest per annum is

(1) 6% (2) 8%

(3) 12% (4) 15%

Answer 1

S.I = P*R*T/100
S.I = 7500*R*2/100 = 150*R...(i)

C.I for 1st year = P*R*T/100 = 7500*R/100 = 75*R...(ii)
P for second year = 7500 + 75*R
C.I for second year = (7500+75*R)*R/100 = 75*R + 75*R^2/100...(iii)
C.I for 2 years = 75*R + 75*R + 75*R^2/100 = 150*R + 3*R^2/4...(iv)

Given, C.I - S.I = 108
(iv) - (i) = 108
108 = 150*R + 3*R^2/4 - 150*R
108 = 3*R^2/4
108*4/3 = R^2
R^2 = 144
R = 12
Hence rate(R) = 12%
Hope it helps.